scholarly journals ON GAMES OF PERFECT INFORMATION: EQUILIBRIA, ε–EQUILIBRIA AND APPROXIMATION BY SIMPLE GAMES

2005 ◽  
Vol 07 (04) ◽  
pp. 491-499 ◽  
Author(s):  
GUILHERME CARMONA
Keyword(s):  
Payoff Function ◽  
Perfect Information ◽  
Perfect Equilibrium ◽  
Simple Games ◽  
Original Game ◽  
Approximation Sequence ◽  
Perfect Equilibria

We show that every bounded, continuous at infinity game of perfect information has an ε–perfect equilibrium. Our method consists of approximating the payoff function of each player by a sequence of simple functions, and to consider the corresponding sequence of games, each differing from the original game only on the payoff function. In addition, this approach yields a new characterization of perfect equilibria: A strategy f is a perfect equilibrium in such a game G if and only if it is an 1/n–perfect equilibrium in Gn for all n, where {Gn} stands for our approximation sequence.

scholarly journals On Perfect Nash Equilibria of Polymatrix Games

Game Theory ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Slim Belhaiza
Keyword(s):  
Nash Equilibria ◽  
Convex Polytopes ◽  
Finite Union ◽  
Perfect Equilibrium ◽  
Small Game ◽  
Dominated Strategies ◽  
Polymatrix Games ◽  
Linear Programming Formulation ◽  
Perfect Equilibria

When confronted with multiple Nash equilibria, decision makers have to refine their choices. Among all known Nash equilibrium refinements, the perfectness concept is probably the most famous one. It is known that weakly dominated strategies of two-player games cannot be part of a perfect equilibrium. In general, this undominance property however does not extend to n-player games (E. E. C. van Damme, 1983). In this paper we show that polymatrix games, which form a particular class of n-player games, verify the undominance property. Consequently, we prove that every perfect equilibrium of a polymatrix game is undominated and that every undominated equilibrium of a polymatrix game is perfect. This result is used to set a new characterization of perfect Nash equilibria for polymatrix games. We also prove that the set of perfect Nash equilibria of a polymatrix game is a finite union of convex polytopes. In addition, we introduce a linear programming formulation to identify perfect equilibria for polymatrix games. These results are illustrated on two small game applications. Computational experiments on randomly generated polymatrix games with different size and density are provided.

scholarly journals Subgame‐perfect equilibrium in games with almost perfect information: Dispensing with public randomization

2021 ◽  
Vol 16 (4) ◽  
pp. 1221-1248
Author(s):  
Paulo Barelli ◽  
John Duggan
Keyword(s):  
Dynamic Games ◽  
Subgame Perfect Equilibrium ◽  
Perfect Information ◽  
State Transitions ◽  
Original Game ◽  
Equilibrium Existence ◽  
Weakly Continuous ◽  
Continuous State ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

Harris, Reny, and Robson (1995) added a public randomization device to dynamic games with almost perfect information to ensure existence of subgame perfect equilibria (SPE). We show that when Nature's moves are atomless in the original game, public randomization does not enlarge the set of SPE payoffs: any SPE obtained using public randomization can be “decorrelated” to produce a payoff‐equivalent SPE of the original game. As a corollary, we provide an alternative route to a result of He and Sun (2020) on existence of SPE without public randomization, which in turn yields equilibrium existence for stochastic games with weakly continuous state transitions.

scholarly journals The Strategic Role of Nonbinding Communication

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Luis A. Palacio ◽  
Alexandra Cortés-Aguilar ◽  
Manuel Muñoz-Herrera
Keyword(s):  
Bargaining Power ◽  
Equilibrium Selection ◽  
Strategic Communication ◽  
Perfect Information ◽  
Perfect Equilibrium ◽  
Truth Telling ◽  
Stag Hunt ◽  
Strategic Role ◽  
Different Levels

This paper studies the conditions that improve bargaining power using threats and promises. We develop a model of strategic communication, based on theconflict game with perfect information, in which a noisycommitment messageis sent by a better-informed sender to a receiver who takes an action that determines the welfare of both. Our model captures different levels of aligned-preferences, for which classical games such asstag hunt,hawk-dove, andprisoner’s dilemmaare particular cases. We characterise the Bayesian perfect equilibrium with nonbinding messages undertruth-telling beliefsandsender’s bargaining powerassumptions. Through our equilibrium selection we show that the less conflict the game has, the more informative the equilibrium signal is and less credibility is necessary to implement it.

scholarly journals The Survival of the Welfare State

2003 ◽  
Vol 93 (1) ◽  
pp. 87-112 ◽  
Author(s):  
John Hassler ◽  
José V Rodríguez Mora ◽  
Kjetil Storesletten ◽  
Fabrizio Zilibotti
Keyword(s):  
Welfare State ◽  
Multiple Equilibria ◽  
Redistributive Policies ◽  
Markov Perfect ◽  
Private Investments ◽  
The Future ◽  
Model Features ◽  
Perfect Equilibria ◽  
The Welfare State

This paper provides an analytical characterization of Markov perfect equilibria in a model with repeated voting, where agents vote over distortionary income redistribution. A key result is that the future constituency for redistributive policies depends positively on current redistribution, since this affects both private investments and the future distribution of voters. The model features multiple equilibria. In some equilibria, positive redistribution persists forever. In other equilibria, even a majority of beneficiaries of redistribution vote strategically so as to induce the end of the welfare state next period. Skill-biased technical change makes the survival of the welfare state less likely.

scholarly journals On the characterization of weighted simple games

2017 ◽  
Vol 83 (4) ◽  
pp. 469-498 ◽  
Author(s):  
Josep Freixas ◽  
Marc Freixas ◽  
Sascha Kurz
Keyword(s):  
Simple Games
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